Recovering the counterfactual wage distribution with selective return migration

Transcription

1 Recovering the counterfactual wage distribution with selective return migration Article Accepted Version Biavaschi, C. (2016) Recovering the counterfactual wage distribution with selective return migration. Labour Economics, 38 (1). pp ISSN doi: Available at It is advisable to refer to the publisher s version if you intend to cite from the work. Published version at: To link to this article DOI: Publisher: Elsevier All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is retained by the creators or other copyright holders. Terms and conditions for use of this material are defined in the End User Agreement. CentAUR Central Archive at the University of Reading

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3 Recovering the Counterfactual Wage Distribution with Selective Return Migration Costanza Biavaschi Forthcoming in Labour Economics doi: /j.labeco Abstract This paper recovers the distribution of wages for Mexican-born workers living in the U.S. if no return migration of Mexican-born workers occurred. Because migrants self-select in the decision to return, the overarching problem addressed by this study is the use of an estimator that also accounts for selection on unobservables. I find that Mexican returnees are middle- to high-wage earners at all levels of educational attainment. Taking into account self-selection in return migration, wages would be approximately 7.7% higher at the median and 4.5% higher at the mean. Owing to positive self-selection, the immigrant-native wage gap would, therefore, partially close if there was no return migration. JEL Classification Codes: J61, F22 Keywords: return migration, self-selection, assimilation, U.S.-Mexico migration. 1 Introduction Migrants self-selection is a core issue in labor economics. If migrants are rational actors optimally choosing their residence location, any observed outcome for this group will be endogenous to the original migration decision. Hence, to understand migrants outcomes it is necessary to understand the nature of their selection. Yet, the literature has primarily viewed migration as permanent, when in fact individual migration is often of a temporary nature. The recognition that migration is a dynamic process has more recently encouraged scholars to understand its drivers (Dustmann, 2003) and its consequences in terms of migrant selectivity (Borjas and Bratsberg, 1996; Dustmann and Weiss, 2007). How do returnees compare with those who Acknowledgements: I would like to thank Corrado Giulietti, Roger Klein, Carolyn Moehling, Anne Piehl, Helena Skyt Nielsen, two anonymous reviewers as well as conference and seminar participants at IZA, NHH and at the 4th AFD-World Bank International Migration and Development Conference for their helpful comments. All errors are mine. Department of Economics, University of Reading, Whiteknights, Reading, RG6 6AA, United Kingdom. c.biavaschi@reading.ac.uk 1

4 permanently settle abroad? Answering this question is consequential for several lines of research. From the destination country perspective, a vast literature has attempted to measure the economic assimilation of immigrants with natives (see seminal work by Chiswick (1978) and papers by Borjas (1985); LaLonde and Topel (1992); Borjas (1994) among others). If selectivity in return migration is not considered, however, the economic progress of immigrants will be over- or underestimated depending on the nature of this selection (Hu, 2000; Lubotsky, 2007). From the source country perspective, return migration may mitigate the brain drain through acquisition of skills used at home (Dustmann et al., 2011). Hence, return migration may help to foster growth in the source country through an expansion in its human capital stock (Dos Santos and Postel-Vinay, 2003). Taking into account selectivity in return migration urges scholars to reconsider how they measure the effects of migration on both immigrants and natives, as well as on both the sending and receiving regions. Building on the previous literature that often analyzes how returnees average earnings differ from those of stayers, this paper combines data derived from U.S. and Mexican censuses to estimate the wage distribution of Mexican-born immigrants in the U.S. under two conditions, namely with and without return migration. This approach enables answering two key questions: how do returnees compare with stayers and where does return migration have its largest impact on the wage distribution? 1 This paper highlights the consequences for the U.S. if no return migration of Mexican-born workers had occurred between 1995 and 2000, shedding light on a counterfactual scenario that could have occurred if incentives to return were altered based on exogenous variations in economic opportunities in the source or host countries. The overarching problem of this study is to recover the counterfactual wage density in the presence of selective return migration, when pre-migration earnings are not known. Crucial to the approach adopted is the introduction of an estimation technique that can recover such distribution, taking into account not only the observable differences between stayers and returnees but also selfselection on unobservables. This paper proposes a semiparametric procedure that complements the estimator presented by DiNardo et al. (1996) applied in the migration literature (Butcher and DiNardo, 2002; Chiquiar and Hanson, 2005), which accounts for selection based on observable traits only. The presented estimation method is based on the observation that selection bias disappears for subgroups where nearly all individuals settle permanently in the U.S. This procedure provides an alternative to the use of pre-migration earnings to measure selectivity, as these are often unavailable to the researcher either due to the lack of longitudinal data following stayers and returnees or because the return flows in available surveys are often too small to allow suitable analysis. Conditioning on observable characteristics, I find that Mexican returnees are middle to high wage earners, consistent with models in which the decision to return hinges on reaching targetearnings levels. Taking self-selection into account, the wages of Mexican born workers in the U.S. would be approximately 7.7% higer at the median and 4.5% higher at the mean. Furthermore, the 1 I assume throughout that the supply effects of the absence of return migration are negligible. Given the negative yet often small impact of migration on the overall economy, this assumption seems to be reasonable. 2

5 return flow has a small effect on immigrant wage inequality: the outflow of immigrants increases dispersion in the lower part of the distribution and decreases it in the upper part. Moreover, selective return migration does not have a constant effect across educational levels: while it increases inequality at low levels of education, it decreases inequality for the highly skilled. These results suggest that when designing optimal migration policies policymakers should consider that selective outmigration might have a greater impact at high levels of human capital. Finally, because at all levels of education the immigrants who leave are the high-wage earners, the immigrant native wage gap would close slightly if there was no return migration. The remainder of this paper is organized as follows. Section 2 reviews the literature. Section 3 describes the data. Section 4 presents the estimation technique and Sections 5 and 6 the results, while Sections 7 and 8 show the sensitivity of the results to different specifications and to the assumptions made. Section 9 concludes the paper. 2 Immigration, Return Migration and Self-Selection across the Mexican U.S. border Several contributions to the immigration literature have empirically assessed the selection of immigrants from Mexico to the U.S., while the literature on the selection of Mexican return migrants is relatively less developed. The current debate on immigrant selection has developed from the results of Chiquiar and Hanson s (2005) which contradict the theoretical predictions proposed in Borjas (1987), showing intermediate to positive selection based on the observable characteristics of Mexican immigrants to the U.S. compared with Mexican stayers in Mexico. Yet the finding of positive selection was challenged by a few authors (Ibarraran and Lubotsky, 2007; Fernandez-Huertas Moraga, 2011; McKenzie and Rapoport, 2010; Ambrosini and Peri, 2012; Kaestner and Malamud, 2014), who have drawn scholarly attention to the importance of two key elements in the analysis of the selectivity of migrants. First, it is crucial to use nationally representative data sources that have a longitudinal component capable of capturing the pre-migration earnings of migrants and nonmigrants (Fernandez-Huertas Moraga, 2011; Ambrosini and Peri, 2012; McKenzie and Rapoport, 2010; Kaestner and Malamud, 2014). Second, researchers must aim to control for the unobservable differences between migrants and non-migrants (Fernandez-Huertas Moraga, 2011; Ambrosini and Peri, 2012). Turning to the selection of returnees, the overall evidence for the U.S. economy suggests that returnees have below average skills. By comparing longitudinal and cross-sectional data, Lubotsky (2007) finds that return migration by low-wage immigrants from the U.S. has systematically led past researchers to overestimate the wage progress of stayers by 10% to 15%. Likewise, Hu (2000) shows a decline in immigrant wage growth once return migration has been taken into account, with such results being weaker for Hispanic workers. Hu (2000) and Lubotsky (2007) both provide interesting insights into the nature of return migration and its impact on the host economy; however, 3

6 in their longitudinal datasets returnees are not directly identified and return migration cannot be separated from other sources of panel attrition. 2 Furthermore, their estimation technique is based on the assumption of time invariant unobserved selection. 3 The previous discussion confirms that self-selection and data availability have limited our understanding of return migration and its consequences. Therefore, in order to fill this gap in the literature, this paper advances an analysis that uses representative data and examines the actual return choices of Mexican migrants based on a dataset that combines data from both U.S. and Mexican censuses. While combining census data to study return migration is not novel and was used in Lacuesta (2010), this study adds to that contribution by controlling for selection on unobservables. The use of two censuses together with the econometric technique proposed allows researchers to distinguish return migration from panel attrition and to treat all those forms of sample selection and heterogeneity that are not simply eliminated by fixed effects estimators in panel data analyses. Furthermore, it provides a full picture of what the U.S. could expect if return migration was zero, owing to changes in either migration policies or migration incentives. On the methodological side, this paper introduces an estimator for a counterfactual distribution that accounts for sample selection. This technique complements the analysis based on selection on observables (Chiquiar and Hanson, 2005; Ibarraran and Lubotsky, 2007) 4 in order to account for selection on unobservables as well. The proposed estimator is based on the model presented by Heckman (1990), and it extends the estimator proposed by Andrews and Schafgans (1998) to its density equivalent. This method could also be applied to other contexts in order to recover a distribution of outcomes that are truncated and/or when panel data are unavailable. 3 Data The analysis presented uses the U.S. and Mexican censuses from 2000, available through the International IPUMS website. 5 The Mexican census was conducted in February 2000 by the Instituto Nacional de Estadística Geografía e Informática (INEGI), the Mexican statistical agency. Household heads were asked to list all current members of the household and to also list their place of 2 In particular, these authors identify non-employment, outmigration, employment in the informal sector, and nonmatch as possible causes of panel attrition. 3 Further analyses from the Mexican perspective include Lacuesta (2010), Ambrosini and Peri (2012) and Reinhold and Thom (2013). Lacuesta (2010) and Reinhold and Thom (2013) both provide evidence of selection and skill upgrading for Mexican returnees in Mexico. Lacuesta (2010) argues that return migrants are similar to stayers, suggesting that the 7% wage premium found upon return might actually be caused by the selection of return migrants that were unaccounted for in the analysis. Meanwhile, Reinhold and Thom (2013), using the Mexican Migration Project (which is not a representative sample), estimate the experiences of returnees to the U.S. labor market by correcting for the endogeneity of migration decisions. They find that returnees are negatively selected in terms of unobservable traits, although selection is not significant in their analysis. Finally, Ambrosini and Peri (2012) find preliminary evidence that returnees are positively selected compared with non-migrants and permanent migrants. However, the results on returnees self-selectivity are based on a very small sample. 4 Chiquiar and Hanson (2005) s estimation is in turn based on DiNardo et al. (1996) 5 Minnesota Population Center. Integrated Public Use Microdata Series, International: Version 6.4 [Machinereadable database]. Minneapolis: University of Minnesota, See international/, last retrieved on June

7 residence in The data consist of a 10.6% sample of the Mexican population and are stratified geographically by municipality and urban area. The U.S. census was conducted in April 2000 and the available data are a 5% random sample of the original forms. It is a weighted sample with stratification by state. Mexican-born immigrants are defined as individuals born in Mexico who appear in the U.S. census. Mexican-born return migrants appear in the Mexican census and are identified as those individuals who report having resided in the U.S. five years prior to the Mexican census enumeration. The data on the returnees in Mexico and the data on the Mexican-born stayers in the U.S. are then pooled to build a dataset containing all individuals who are or have been in the U.S. For comparison purposes, this study also uses data on a random sample of U.S. native-born workers (n = 103,994). 6 However, the use of different data sources to identify return migrants is not without limitations. As discussed in Chiquiar and Hanson (2005) and Ibarraran and Lubotsky (2007), the most notable drawbacks relate to changes in education once in the U.S., the misreporting of education in the U.S. census, and undercount due to illegal immigration and short trips. Given that this study focuses on return migration, the possibility of Mexican immigrants having obtained additional schooling after arriving in the U.S. should not be regarded as invalidating since returnees could have made the same choice. Nonetheless, the concern remains that Mexican migrants in the U.S. might overstate their levels of educational attainment (Ibarraran and Lubotsky, 2007). I will further discuss this issue when checking the robustness of the results. The undercount of illegal immigrants and shortterm migrants in the U.S. census might indeed constitute a problem, which is discussed in Section 7. Finally, there is a further concern specific to this study: the universe of returnees is much broader than is captured by the Mexican census. If Mexican workers who returned before 1995 systematically differ from those who returned between 1995 and 2000, the conclusions of this paper would not be externally valid. Since no further information is available on workers having been abroad, looking at place of residence in 1995 is the best proxy for return status. 7 The sample is restricted to men aged between 25 and 55 years, born in Mexico, and in earning employment, resulting in a total sample size of 133,389. Of this number, 120,205 (90%) immigrants stay in the U.S., while 13,184 (10%) are return migrants. This study applies four indicators of educational attainment (Less than primary school completed, Primary school completed, Secondary 6 I have run exploratory analyses to understand whether the use of weighting in each sample affected the conclusions of the paper. Results are comparable with those reported in the analysis, and in particular the selection of individuals with a high probability of staying is unaffected by the weighting procedure. The sampling criteria of the censuses are unlikely to be related with the decision to stay or with the error term in the wage equation. If the reader is concerned about the geographical stratification, the full model estimated in Section 7 should reassure that results are stable once we control for geography. In choosing not to use weight, the results are directly comparable with those in the literature (Chiquiar and Hanson, 2005; Lacuesta, 2010). Additional details on sampling issues are discussed in Section 7. 7 The 1990s were a decade of radical transformation in the Mexican economy, with the signing of the NAFTA in 1994, the Mexican peso crisis in , and the subsequent period of macroeconomic growth. It is, therefore, possible that changing macroeconomic conditions affected the return migration flow. However, it remains of interest to study the return phenomenon during periods of financial turmoil, as public opinion might have particular sentiments about migrants prolonging their stays in the U.S. Finally, a parametric analysis of selection in 1990 shows a similar pattern of return migration. These results are available upon request In addition, Section 7 further shows how selection patterns persist when looking at return migration in the early 2000s. 5

8 school completed, College Degree), while socioeconomic characteristics are represented by indicators of being married (Married), having children (Child), and having a U.S.-born spouse (Spouse U.S.- born) or child (Child U.S.-born). The decision to stay in the U.S. is modeled throughout this analysis as a function of these educational and socioeconomic variables. Table C.1 in the Appendix reports the characteristics by return status. 8 The wage process is modeled according to various specifications. In the first set of regressions the observable characteristics include those regressors used in previous analyses on Mexican-U.S. selection, namely, education, age and family status (Fernandez-Huertas Moraga, 2011; Ambrosini and Peri, 2012; McKenzie and Rapoport, 2010; Lacuesta, 2010; Kaestner and Malamud, 2014). Moreover, the indicator of having a U.S.-born spouse is included to capture the constructs of attachment and networks, which have both been shown to be relevant determinants of migration decisions (McKenzie and Rapoport, 2010; Ambrosini and Peri, 2012). Having a U.S.-born child is also included in the model for the decision to stay, yet is excluded from the wage equation. To summarize the effects of these characteristics on the wage distribution, Figure 1 applies the methodology developed in DiNardo et al. (1996) to show the actual distribution of wages for Mexican-born workers in the U.S. and the distribution of wages that would have occurred if U.S. stayers shared the observable characteristics of returnees and were paid according to U.S. skill prices. [FIGURE 1 HERE] Figure 1 illustrates that the counterfactual distribution is shifted to the left compared with the actual distribution observed in the U.S.: therefore, returnees appear to be negatively selected in terms of observable characteristics. Consequently, based on observable traits, the figure suggests that returnees are drawn disproportionately from the bottom part of the wage distribution. Section 4 explains how a counterfactual distribution can be estimated if all returnees had stayed, by accounting for both observable and unobservable traits. The remainder of the paper subsequently compares the counterfactual results with the descriptive analysis presented in this section. 4 The Model and the Estimation Strategy The research question answered in this study requires recovery of the wage distribution for all Mexican-born men who have been in the U.S., despite wages only being observed for Mexican-born immigrants who are currently residing in the country. Let S i be an indicator of whether or not 8 Table C.1 in the Appendix reports also the average characteristics of other variables used in the analysis. Experience in the U.S. is represented by indicators of length of stay between 0 and 5 years, 5 to 10 years, 10 to 20 years, 30 to 40 years, and more than 40 years (Years in the U.S.). The limited information collected by the Mexican census about returnees experiences abroad means that how long these workers stayed in the U.S. before returning to Mexico is unknown. Regional labor market characteristics are represented by indicators of residence location in four regions: West, Northeast, Midwest, South. Fourteen industry variables are also reported. The table further reports the average wages of U.S. stayers. The wage variable is constructed as wage and salary income divided by hours of work. To avoid division bias (Borjas, 1980), earnings were also used as the dependent variable, without changes to the conclusions of the paper. The average wage in the U.S. for returnees is unobserved. 6

9 individual i decides to stay in the U.S. In the following model this decision depends on the net benefits of staying, (Z i α 0 ɛ i ), being greater than zero. Let r be the number of returnees and n be the number of stayers. The decision to stay can be represented as: 1 Z i S = α 0 > ɛ i for i = 1,..., r + n (1) 0 Z i α 0 ɛ i The true wage determination process for a randomly selected Mexican immigrant present in the U.S. takes the form: Y i = X iβ 0 + c 0 + u i i = 1,..., r + n. (2) In the model, Yi is the log of the hourly wage for Mexican immigrants, and X i represents the determinants of the log-wage process. The wage is observed only for those immigrants who stay in the U.S., however. In other words, the observed wage is: Y i = S i Y i i = 1,..., r + n. (3) From the model in equations (1) and (2) it follows that (Y, S i, X i, Z i ) are observed random variables. observed. The aim of the estimation is to obtain the distribution of Yi, given that only Y i is For generality, the remainder of the paper focuses on estimation techniques that are free from distributional assumptions, while a comparison with the parametric model is reported as a robustness check. Using flexible estimators is particularly important whenever the parametric assumptions are not satisfied. It is assumed throughout that (X i, Z i, u i, ɛ i) are i.i.d and (X i, Z i ) are exogenous random variables. It should be stressed that u i and ɛ i are allowed to be correlated. Section 7 discusses these assumptions. The next subsection introduces the estimation strategy. 4.1 Counterfactual Density Estimation The distribution of Yi in equation (3) corresponds to the distribution of u i up to a location shift represented by the observable characteristics, (X i β 0 + c 0 ). Hence, the estimation strategy of the counterfactual wage distribution entails two steps: 1. Recover the distribution of the unobservables, f(u ) 2. Recover the full distribution of wages by shifting f(u ) by the mean of (X i β 0 + c 0 ). At this stage all observable differences between stayers and returnees are considered and taken into account. Because the key challenge and contribution of the paper lies in recovering f(u ) (step 1), while standard techniques can be adopted to estimate β 0, c 0 (step 2), the following discussion largely 7

10 focuses on recovering the distribution of u i. Let f(u i ) be the unknown distribution of u i. By the Law of Total Probability, f(u i ) can be written as a weighted sum of the distribution of the error terms in the subsamples of stayers and returnees with weights given by the probability of being in either subsample, i.e.: f(u i Z iα 0 ) = f(u i S i = 1, Z iα 0 ) Pr(S i = 1 Z iα 0 ) + f(u i S i = 0, Z iα 0 ) Pr(S i = 0 Z iα 0 ), I will assume throughout that f(u i S = 1, Z i α 0) = f(u i S = 1) and similarly f(u i Z i α 0) = f(u i ). The analysis is carried out under this assumption for computational speed and expositional purposes. Independence is, however, not necessary. The results are similar when conditioning on particular quantiles of the selection index, as further discussed in Section 8. This density cannot be directly estimated using the sample wage distribution, as the latter is only observed conditional on the decision to stay. In other words, it is not possible to directly obtain an estimate of f(u i ) as no information can be directly extrapolated from the data about the unobservable component of the returnees wage equation. Otherwise stated, f(u i S i = 0, Z i α 0) is unknown. However, note that whenever Pr(S i = 1 Z i α 0) is close to 1, f(u i Z i α 0) = f(u i ) f(u i S = 1, Z i α 0) = f(u i S i = 1). Intuitively, selection disappears in the limit for individuals for whom Pr(S = 1 Z i α 0) is close to 1, namely for those individuals in a high probability set. While it is not possible to know the wage distribution of the returnees, we can still recover the counterfactual distribution out of a subsample for which the likelihood of staying is very high. This intuition is known as identification at infinity (Chamberlain, 1986). Identification at infinity has been advocated by Heckman (1990) to estimate the constant term in semiparametric sample selection models and Andrews and Schafgans (1998) develop an estimator in the spirit of the one proposed by Heckman. 9 Several applications have relied on this identification strategy to recover the constant term in sample selection models, ranging from studies of gender (Schafgans, 2000; Martins, 2001; Mulligan and Rubinstein, 2008; Albrecht et al., 2009; Chzhen and Mumford, 2011) and ethnic wage differentials which correct for labor force participation choices (Schafgans, 1998), to the estimation of wage differentials for union and non-union members (Lanot and Walker, 1998), to the effects on children s BMI of mothers labor force participation choices (Liu et al., 2009), to health care utilization differences among insured and uninsured workers (Shen, 2013). In all these examples, the constant is recovered out of a subset of individuals for which selection is unlikely to occur, i.e. groups with fairly high participation rates (older, urban workers with secondary degrees), likely to be unionized (older, semi-skilled workers) or insured (individuals with several co-morbidities working in industries with high insurance rates). As long as the characteristics Z that select the sample are exogenous and observations are i.i.d., focusing on particular groups where selection disappears should deliver a consistent estimate of the quantity of interest. In my context, this idea will be used to recover f(u ). Applying this strategy, estimation of the distribution of 9 Schafgans and Zinde-Walsh (2002) prove the asymptotic properties of Heckman s (1990) proposed estimator for the intercept in a sample selection model, while Klein et al. (2015) extend these results to allow for a definition of an high probability set that is data-dependent. 8

11 unobservable characteristics is based on a subsample selected on observed characteristics Z, in which nearly all individuals stay in the U.S. To the best of my knowledge, such an identification strategy has not been applied to recover a counterfactual distribution, as is carried out in this paper, in order to allow for selection on unobservables in a counterfactual density estimation. Let H i be an indicator that defines whether the observation is in this high-probability set, i.e. let H i = 1[Pr(S i = 1 Z i α 0) > p n )]. The proposed estimator for f(u i ) is: ( ) n f(u i ) = i=1 1 h K u u i h S i H i n i=1 S, (4) ih i where K( ) is a kernel density estimator and h is the bandwidth parameter. A Gaussian kernel with optimal bandwidth h = 1.06ˆσN 1/5 (Silverman, 1986) is chosen throughout the paper when reporting the densities of interest. This estimator is simply a kernel density estimator of the random variable u over a proportion of observations for which the probability of being in the selected sample is close to 1 at the limit. A Monte Carlo is reported in Appendix A to explain how well this method works. 4.2 Parameter Estimation To estimate the density in equation (4), unbiased estimates of the parameters in the model (α 0, β 0, c 0 ) must be obtained in order to construct the residuals, û. To study the S i choice, I estimate a semiparametric dichotomous choice model, 10 by applying the estimation method developed by Klein and Spady (1993). This estimator is the semi-parametric equivalent of a standard logit or probit model. In fact, the parameters of interest are estimated by maximizing a log-likelihood function where the probability of staying in the U.S. is a semiparametric expectation function of the singleindex Z i α, rather than a parametric probability in a logit/probit form function of the same index. Therefore, the likelihood function takes the standard following form: ln L = n S i ln( ˆP i (v i )) + (1 S i ) ln(1 ˆP i (v i )), i=1 where v i is the selection index Z i ˆα hereafter. In the construction of the likelihood, some of the observations for which this probability is poorly estimated are trimmed. 11 To estimate ˆP, I apply the bias correction technique proposed by Klein and Shen (2010) to overcome finite sample performance issues. 12 While the original formulation of Klein and Spady assumes that one of the variables in 10 On the contrary, DiNardo et al. (1996) choose to adopt a parametric specification for their selection model (hence, their approach is deemed to be semiparametric). For coherence, I estimate all parts of the model without any distributional assumptions. In Section 5, however, I also present parametric estimates for comparison. 11 Trimming is standard in this literature. 12 Both in Klein and Spady (1993) and in Klein and Shen (2010), the bandwidth h is set to satisfy n 1/6 < h < n 1/8. Specifically, I set h = n 1/7. Additionally, it should be noted that in the estimation of the selection index, the only identified parameter in terms of the original model is the coefficient ratio, i.e., α j/α 1, with j = 1... k and where α 1 is the coefficient of the continuous variable, which is normalized to 1. 9

12 the index is continuous and with non-zero coefficient to reach identification of the semiparametric expectation, subsequent work in Delgado and Mora (1995) and Klein and Shen (2010) suggests that this assumption is sufficient but not necessary for identification, provided tail conditions on the density for the dependent variable are satisfied. In this application, I have used the variable Age as normalization variable. Age takes 31 distinct values, and Monte Carlo simulations available upon request on the performance of the Klein and Spady estimator in my setting show that this variation is sufficient to identify the parameters of interest. The recovery of Z i ˆα is useful for two reasons. First, it is now possible to select those observations in the high probability set, for which selection can be ignored at the limit. Thus, individuals in the high probability set represent those observations in the 95th percentile of Pr(Si = 1 Z i ˆα).13 Second, the estimation of (Z i ˆα) allows us to obtain unbiased estimates of the outcome equation parameters. In the wage equation, I employ Robinson s (1988) differencing method in order to correct for sample selection and recover unbiased estimates of β 0, as well as the estimator proposed by Heckman (1990) to recover c 0. Before proceeding to the results, one identification issue must be discussed. At least one variable is needed in the Z i matrix that does not appear in the X i matrix. The variable included in the selection process and excluded from the wage process is having a U.S.-born child, which proxies for social attachment to the destination country. Because the idea of attachment to people and institutions in the destination country raises the opportunity cost of returning, this should act as a strong predictor of this choice. However, it is unlikely that the wage process depends on the birthplace location of an individual s children. 14 Consequently, the effect of having a U.S.-born child should not predict an individual s wage, after controlling for attachment and network effects through the U.S.-born spouse indicator and length of stay in the U.S. variable Potentials and Limitations of the Estimation Strategy Primary assumptions are that (X i, Z i, u i, ɛ i) is i.i.d and that the regressors are exogenous. These are common assumptions of standard empirical models in the migration literature. In fact, the mean independence of the error term from the explanatory variables in the outcome and selection equations is typical in linear regression models (Lacuesta, 2010; Reinhold and Thom, 2013; Kaestner and Malamud, 2014) and in the non-parametric analyses based on pre-migration earnings (e.g., Ambrosini and Peri, 2012; Fernandez-Huertas Moraga, 2011) as selection is here recovered only if the subdivision into cells is exogenous. 16 These models further conjecture the absence of an 13 Although this cut point is arbitrary in the paper, results are stable when a different definition of the high probability set is used. Such results are available upon request. 14 Additional regressions also controlled for the language spoken at home. Having a U.S. child might be related to an individual s wage if English proficiency is enhanced by the presence of a child at home. The results that control for this additional variable do not differ from those presented in the paper, and they are available upon request. 15 Additional evidence and discussion on the validity of the exclusion restriction can be found in Section As already mentioned, the variables used here to identify individuals that have a high probability of staying are similar to those used to identify cell-probabilities in other studies. 10

13 Ashenfelter dip, and that expectations of migration and return do not influence the individual s behavior before migrating. The above estimator avoids these hypotheses as it does not use premigration earnings to measure selection. Nevertheless, it imposes a structure between the outcome and observable traits and a stronger need for identically distributed observations. This assumption is further discussed in Section 7. While the estimation strategy is not a replacement for other analyses, the estimator in this paper could be advantageous in certain circumstances. Such scenarios include whenever the data provide insufficient information on returnees wages, such as in Census data (as in this paper and in Lacuesta, 2010; Ambrosini et al., 2015), when the sample size is too small to guarantee sufficient statistical power to the analysis (Ambrosini and Peri, 2012), or as a robustness check for the presence of feedback effects on the migration decision or Ashenfelter dip whenever pre-migration earnings are indeed observable, as in Fernandez-Huertas Moraga (2011), Ambrosini and Peri (2012), McKenzie and Rapoport (2010), and Kaestner and Malamud (2014). 5 Results In addition to interest in the counterfactual estimation, the data enable studying different components of the return choice, as well as the wage determination process for Mexican-born immigrants in the U.S. Subsection 5.1 studies these choices, while Subsection 5.2 presents the density estimation results. 5.1 Parameter Estimates The estimates of the marginal effects for the observable characteristics determining the decision to stay in the U.S. are presented in Table 1. Because these marginal effects are computed at the mean, the first column of the table reports the average characteristics of the immigrant sample. [TABLE 1 HERE] Each additional year of age has only a small effect on the probability of staying, increasing it by 0.4%. Compared with uneducated individuals, Mexicans who have completed primary (secondary) school are approximately 2% (6.7%) more likely to stay, while Mexicans with a college degree are approximately 3% more likely to stay. Having a foreign-born spouse slightly reduces the probability of staying, while individuals with a U.S.-born spouse are approximately 5% more likely to stay compared with those that have a foreign spouse. Meanwhile, having a foreign (U.S.)-born child reduces (increases) the probability of staying by approximately 6% (17.5%). It should also be noted that the two variables indicating social attachment to the host country are strongly significant, and based on observable characteristics stayers are more likely to have better educational outcomes. In addition, Figure 2 shows the actual and predicted share of stayers as we change the observable characteristics (as represented by decile of the index) and the distribution of the 11

14 predicted probability of staying in the U.S. Overall, the model fits the data well and the probability of staying in the U.S. takes a wide range of values. Following Robinson s (1988) estimation, the procedure explained above also produces results for the wage process. These results are presented in Table C.2 in the Appendix and show standard labor market premia of the various individual characteristics. In estimating the counterfactual density of interest, I use a parsimonious specification where wages are estimated conditional only on demographics and socioeconomic characteristics such as educational attainment and family status. The results, based on a full set of controls, are reported as a robustness check in Section 7. The estimation of the selection equation allows selecting those individuals for which sample selection disappears, namely, those individuals in the high probability set. As mentioned in the previous section, individuals with a high probability of staying need to be selected. Table 2 shows the characteristics of the individuals inside and outside this high probability set. These individuals are on average more educated and more likely to have a U.S. born child and spouse. It should be noted that these differences will be taken into account when constructing the wage distribution in the next section. Instead, the main identifying assumption is that the selection of this subsample is exogenous. In the robustness checks section, I will further comment on the evidence of Z being exogenous. 5.2 Density Estimates The following three research questions will now be answered in turn: (i) how different is the full immigrant population in terms of observable and unobservable traits compared with the population that stays in the U.S.; (ii) what would the distribution of wages be in the absence of return migration; (iii) how does this distribution change, conditional on educational characteristics? How different is the immigrant population from the population of stayers in the U.S., in terms of observable and unobservable traits? Table 3 reports the deciles of the predicted wage, the residuals and the wage process that are observed and that would have been observed had there been no return migration. These quantities were calculated in the following manner. The first panel shows the predicted actual and counterfactual wages, both calculated as the product of the returns on the skills reported in Table C.2 and the characteristics of immigrant stayers (immigrant population) characteristics for the actual (counterfactual) predicted wage distribution, i.e., ĉ + ˆβX j, where j = only stayers, immigrant full population. I then report the average ĉ + ˆβX j in each decile of its distribution. The second panel reports the average estimated residuals in the actual and counterfactual distribution, by decile. As explained in Section 4.1, these were estimated from the high probability set. The last panel shows actual and counterfactual wages. Here I consider the distribution of the residuals and shifts it by the average predicted wages in the actual and counterfactual scenarios (that is, by the mean of ĉ + ˆβX j ). The deciles of the predicted wage are therefore reported as a summary measure. Because at all deciles the full population has higher unobservable characteristics than the selected population, as well as only marginally 12

15 lower observable skills, the wage distribution of the population will lie to the right of the observed distribution among the stayers, even if other quantiles were used. [TABLE 3 HERE] In terms of observable characteristics, Mexican immigrants would on average earn less had there been no return migration. In fact, the log-difference across the different deciles is always negative, which is in line with the descriptive analysis that found returnees to have below average skills. However, these differences are relatively small, reaching at most a decrease of a few cents (approximately 0.8%) in the wages between the two scenarios, because returnees represent only a small proportion of the total immigrant population. The role of unobservable traits is shown in the second panel of Table 3. Unobservables were calculated as the difference between the actual and the predicted wages for the stayers, and were directly estimated for the full population using the estimation technique described in Section 4. I find that the positive differences between the counterfactual and actual distributions are driven by dissimilarities in unobservable traits. Had there be no return migration, the immigrant population would have been earning approximately 7.7% more (approximately 1 dollar, at the median) due to unobservable differences between stayers and returnees. The effect at the average level is a 4.5% change in wages, which is consistent with the relatively small effect of selection at the mean reported in previous studies (Lindstrom and Massey, 1994; Ambrosini and Peri, 2012). The evidence presented suggests that immigrant stayers and the full population (i.e. stayers and returnees) are somewhat close in terms of observable traits, whereas differences arise in terms of unobservable traits. In particular, despite returnees being a disadvantaged group in the labor market in terms of observable traits, their unobservable abilities seem to compensate for this lack of skills. Furthermore, it seems that unobservable motives might push returnees to be more successful in the host country than the immigrants who stay. Although we cannot directly explain the motives behind returns, it is possible to conjecture that these immigrants leave the host country upon reaching their savings or skills acquisition goals and that more motivated immigrants are able to meet their personal objectives despite their original disadvantages in the host country labor market. 17 What would the wage distribution be in the absence of return migration? The overall impact of return migration is presented in the last panel of Table 3, which reports the deciles of the actual wage distribution for stayers and those of the counterfactual wage distribution that would have occurred in the absence of return migration. In practice, this second distribution sums the average observable traits (panel one) and the unobservable components (panel two) for the immigrant population at each decile. As differences primarily arise due to the positive difference in the unobservable characteristics of the two populations, the implied counterfactual distribution 17 Yang (2006) explores the reasons behind the returns of Filipino migrants and finds that while lifecycle considerations often motivate return migration, some migrants are motivated by target earnings considerations. 13

16 suggests that Mexican immigrants would be earning more had there been no return migration. In particular, more people would be earning above the median level. Figure 3(a) presents the actual and counterfactual distributions described graphically in order to better visualize them. Although relatively close to each other, some differences in the two distributions are apparent from this figure. In the absence of return migration, more Mexican immigrants would appear in the upper tail of the distribution, thereby increasing the average wage in this population. To better observe this point, Figure 3(b) presents the difference between the counterfactual and actual distributions. Without return migration, more mass would appear in the upper tail of the wage distribution, as the wage difference is shown to be first negative and subsequently positive. Therefore, the disadvantage that returnees face in terms of lost human capital skills is balanced by the higher unobserved motivation and productivity displayed by this group. Overall, this balance translates into an increase in the concentration of individuals in the middle to upper part of the wage distribution in the absence of return migration. A Kolmogorov-Smirnov (KS) test for the difference between these two distributions delivers a D statistic of 3.05, implying that the actual and counterfactual distributions are different at all conventional significance levels. [FIGURE 3 HERE] This finding is not the only insight from the analysis, however. The last panel in Table 3 shows that return migration also affects wage inequality, reporting the 90-10, 90-50, and wage gaps for the actual and counterfactual distributions. At the bottom of the distribution, the absence of return migration would imply an 7.3% increase in the difference between the 50th and 10th percentiles, whereas a reduction in this dispersion would occur at the top of the distribution. Overall, inequality within the Mexican population would increase slightly in the absence of return migration. Therefore, because selective return migration encourages high-wage earners to leave, this leads to a reduction in inequality within the Mexican population remaining in the U.S. By contrast, if all returnees were to stay, the full wage distribution in the population would display a slightly higher dispersion compared with that previously observed. How does the wage distribution change conditional on educational characteristics? Since an individual s educational attainment greatly affects both his or her decision to stay and his or her wage, the importance of selection might vary by educational level. I therefore generate a distribution of unobservables specific to each education group. In other words, the unobservables are now based on a sub-sample of the high probability set with varying levels of education (primary, secondary, tertiary) and I compare these distributions to that of the actual stayers. 18 Accordingly, Table 4 reports the deciles of the predicted wage, unobservables and actual wage distributions for people with a primary school education, high school education and college degree. As before, 18 These distributions are based on 448 observations for individuals with primary education, 6043 observations for the category of secondary educated and 180 observations for individuals with tertiary education. Because the vast majority of observations falls in the second category, it is unsurprising that the actual and counterfactual distributions are closer for this group. 14

17 the differences in observables are negligible across all educational groups, while unobservables are shown to drive dissimilarities in the wage process. [TABLE 4 HERE] However, despite the fact that returnees with primary- and secondary-level educations tend to show higher unobservable traits, the distribution of unobservables is different for college graduates. Figure 4 shows the dissimilarities in the actual and counterfactual distributions at different educational levels in order to better visualize these differences. Figures 4(a) and 4(b) first show the distribution of log-wages for low-educated individuals: as before, returnees are disproportionately drawn from the upper tail of the density. The same conclusion can be inferred from Figures 4(c) and 4(d), which show the same distribution for workers that have a secondary-level education. Finally, Figures 4(e) and 4(f) show what would have happened if all returnees with a college degree had stayed. In this case, a much larger mass of individuals would appear at the center of the distribution. [FIGURE 4 HERE] The findings presented above suggest two main conclusions. First, not all returnees are low-wage earners. In other words, within each educational group some returnees are high earners. Second, most of the action happens at the tails of the distribution: while almost no differences can be detected for individuals educated to secondary level, selective return migration has a much larger impact on individuals with either a low or high level of education. 6 Discussion and Policy Implications In the absence of return migration, more Mexican immigrants would appear in the upper tail of the wage distribution. The results presented in Section 5 suggest that those immigrants who decide to leave are high-wage earners. Consequently, without return migration, the average wage in the population would be higher. This is not only true overall, but also when considering different education levels within the immigrant population. Despite the returnees being less skilled in comparison with stayers, they have higher unobservable traits that make them more successful in the labor market. This finding implies that an analysis that simply controls for differences in observable characteristics might draw the misleading conclusion that returnees are those who fail in the host country. On the contrary, returnees are not failures, but rather those who reached their goals in the host country, either in terms of savings or in terms of skills acquisition. These important results extend the findings of Lubotsky (2007) and Hu (2000). In particular, Lubotsky (2007) shows that negative selectivity is less predominant in the Hispanic population, but the author was unable to explain this finding because of the impossibility of identifying the subsample of Mexican workers in the data. Furthermore, the results are also in line with the conclusions of Ambrosini and Peri (2012), who found indicative evidence of positive selection based on the pre-migration earnings of returnees compared with immigrant stayers despite the use of a 15